My Cool Visualizations
Sina Sajjadi
Background
Here are some cool data visualizations and schematic model descriptions I have created for my past and present projects, mostly using Python and matplotlib. I store them here for future references.
Research
Epidemics on Dynamic Networks of Segregated Communities
To study the racial disparities in COVID-19 infection, we applied a game-theoretical model on top of a spreading process occurring on a stochastic block model network to predict the racial disparity of infection observed in Chicago.
We won the \(2^{nd}\) project award for this research in the Exploring Network Epidemiology in the Time of Coronavirus, online workshops held by University of Maryland and Vermont’s Complex Systems Center among 29 groups. Project title: Racial disparities in COVID-19 cases: Beyond inherent vulnerability.
Figure 1. Segregated Spreading
Blue, red and gray respectively signify \(S\) (Susceptible), \(I\) (Infectious) and \(R\) (Recovered) states. Squares, circles and triangles respectively denote agents from low, middle and high SES communities. The green dash-dotted circles indicate staying home. Solid and dashed lines demonstrate connections capable and incapable of disease transmission.
Karate Club
In this work, by modeling the balance dynamics on empirical social networks, such as Zachary’s karate club (1), we study the effect of heterogeneity on microscopic parameters of the system such as the mean value (+1, -1) of each dyad. We plan to proceed to formulate a mean-field approximation for this dynamics.
Figure 2. karate-club
Each point denotes an edge of the Zachary’s karate club, with \(k_<\) and \(k_>\) indicating the degrees of nodes on each side of the edge. Color code demonstrates \(T_c\) the transition temperature of the edge. Considering that multiple edges may have same couple of values for \(k_<\) and \(k_>\), for demonstration purposes, the points denoting these edges are arranged in a circular manner and encircled by a gray dashed ring.
Epidemics on Empirical Dynamic Networks
By using different shuffling methods and categorizing the results using k-means clustering we studied each correlation’s effect on hindering/enhancing the spreading phenomena. We observed that causal temporal correlations reduce the size of an outbreak, on the other hand, periodical correlations which can either decrease or increase the probability of an outbreak, have no significant effect on the size of a possible outbreak.
Figure 3. Spreading on Dynamic Networks
The figure demonstrates, how the k-means clustering measure works for our purpose. As an example, we see the coinfection dynamics on a shuffled hospital network. The left panel shows the density of the \({ab}\) population, and the probability that a realization settles on the given value of the density (\(\pi ( \rho_{ab}(p) )\): color code) while varying p, which is the first infection probability. The gray dashed curve demonstrates the average \(\rho_{ab}\). The middle panel distinguishes precisely the two epidemic branches in the left panel at \(p=0.069\), the vertical window. The right panel shows the fraction of individuals recovered from one disease (x axis) and from both diseases (y axis), within each realization. Each point denotes a single realization and different colors indicate different clusters: red (double infection outbreaks), green (single infection), blue (no outbreaks). The dashed shapes, encircle the realizations which make up the outbreak branch (OB) in each illustration. The number of realizations is 50000, but for illustrative purposes in the right panel, only a sample of 5000 realizations is depicted.
Figure and caption taken from our paper (2).
Generated by my software 
Available under GPL-3.0 at this repository.
Epidemics on Pedestrian Dynamics
In this work we define a novel type of social distancing (keeping distance from other agents to avoid infection) based on the pedestrian dynamics. We consider both direct and indirect transmission by taking into account the role of environment as a vehicle of spreading. By categorizing the population in three different compartments: \(S\) (Susceptible), \(I\) (Infectious) and \(E\) (Exposed) we simulate the spreading, and predict the risk of infection for different levels of social distancing in multiple scenarios.
The circles denote agents. Blue, red and gold respectively signify \(S\) (Susceptible), \(I\) (Infectious) and \(E\) (Exposed) states. The purple tiles demonstrate the contaminated environment. The green diamond is the target which the infectious agent tries to reach.
Teaching
Schelling Model
Figure 5. Schelling Model
Presented at Schelling Algorithm Implementation and Visualization workshop.
References
1. Wikipedia contributors. Zachary’s karate club — Wikipedia, The Free Encyclopedia. https://en.wikipedia.org/w/index.php?title=Zachary%27s_karate_club&oldid=967105030; 2020.
2. Sajjadi S, Ejtehadi MR, Ghanbarnejad F. Impact of temporal correlations on high risk outbreaks of independent and cooperative SIR dynamics. arXiv:2003.01268 [physics, q-bio] [Internet]. März 2020; Verfgbar unter: http://arxiv.org/abs/2003.01268